GenoDRPh
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Dieter
August 4th, 2022 at 12:52:39 PM permalink
Hello All,

Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene
Dieter
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August 4th, 2022 at 1:45:56 PM permalink
I know some bar dice variants allow partial rerolls, like yahtzee.
Is that allowed, so you can hold a pair, and reroll the other 3 dice?

You say a 3 of a kind gets a "free roll".
Does that mean you roll all 5 dice again?
May the cards fall in your favor.
camapl
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August 4th, 2022 at 2:18:49 PM permalink
Good questions, Dieter!

Also, is any money added to the pot after it hits, or does it start from zero? What happens when someone rolls a four of a kind with less than $100 in the pot (think multiple hits in short succession)?
Expectation is the root of all heartache.
gordonm888
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August 4th, 2022 at 2:39:20 PM permalink
Quote: GenoDRPh

Hello All,

Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene
link to original post



Welcome to the forum! It's always good to take a peek at the forum rules: Forum Rules.

The analysis you are asking for is straightforward and relatively easy. I'm busy and can't do it right now, but I'm sure someone will step up shortly.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
GenoDRPh
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August 4th, 2022 at 3:12:14 PM permalink
Thanks everyone for your responses. I may have left out some crucial information, which I realize after reading my original post. A free roll means you can roll all five dice again, but you must roll all 5 dice. All wagers go in to the pot, which increases with each bet-so I guess you can call that progressive. There's no rake to the house with each bet, other than the 15% to the bartender(s) on duty on a 5 of a kind. As an aside, I've never seen anyone other than one or both of the two ladies who own the place work behind the bar, so maybe you can call that a rake of a sort. I don't know where the seed money for pot comes from, but let's assume that the house puts up a few bucks-let's say to always keep the pot at $200 minimum. I've never been in there when someone's won anything, and have seen the pot in the thousands. Someone did win a bit over $5k once, but I wasn't there, do not know how long the game went without a jackpot winner and the next time I went in the jackpot was a bit over $900.

Gene
Dieter
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August 4th, 2022 at 4:21:57 PM permalink
Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
May the cards fall in your favor.
unJon
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August 4th, 2022 at 7:17:29 PM permalink
Quote: Dieter

Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
link to original post



Itís lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Dieter
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August 4th, 2022 at 7:25:55 PM permalink
Quote: unJon

Quote: Dieter

Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
link to original post



Itís lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.
link to original post



... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.
May the cards fall in your favor.
unJon
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August 4th, 2022 at 7:44:19 PM permalink
Quote: Dieter

Quote: unJon

Quote: Dieter

Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
link to original post



Itís lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.
link to original post



... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.
link to original post



I donít follow that comment. You know the prize pool when you roll. One person rolls at a time.

6^5 = 7,776 ways to roll 5 dice.
6 ways to roll 5OAK
150 ways to roll 4OAK
1,500 ways to roll 3OAK (includes full houses)

Pot is $X

6 * 0.85 * X + 150 * 100 + 1,500 * Y - (7,776 - 1,500 - 150 - 6) = 0

Y is recursive EV of playing the game again. Will calculate when back in front of Excel.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
unJon
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August 4th, 2022 at 8:26:18 PM permalink
I take it back. The game doesnít make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldnít build, it should drain from the 4OAKs.

What am
I missing?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Dieter
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August 5th, 2022 at 3:31:50 AM permalink
Quote: unJon

I take it back. The game doesnít make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldnít build, it should drain from the 4OAKs.

What am
I missing?
link to original post



Dang.

Well... guess I need to go look for a pub. ;)

(I will not use any superpowers in furtherance of this effort. I also know that a common rule is 1 shake per day.)
May the cards fall in your favor.
gordonm888
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August 5th, 2022 at 7:37:00 AM permalink
Quote: unJon

I take it back. The game doesnít make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldnít build, it should drain from the 4OAKs.

What am
I missing?
link to original post



My analysis agrees with unjon's posts. Perhaps something in the statement of the rules isn't accurate?.

Are we sure that any 4oak pays $100, and not just four 6s? Or, that the first 4 dice must be a 4oak?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
camapl
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August 5th, 2022 at 10:52:34 AM permalink
Donít the odds change the more you drink? That must be it, since you only see this game at bars!
Expectation is the root of all heartache.
charliepatrick
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August 6th, 2022 at 12:28:37 PM permalink
The maths sorts of works if you roll one die at a time and lose once you fail to get the recent roll to match.

The first roll is irrelevant. The second roll has to match the first roll to allow a third roll (P=1/6). The third roll has to match, else you lose. You earn a free roll (unless your fourth roll matches). (So the probability of this is 1/36 - 1/216 = 5/216, I have assumed you have the option of having your $1 returned for the break-even point.)

Fourth matching roll earns $100 (probability of this is 1 in 216, but you take off the probability of jackpot to give 5/1296) so this represents about 38.58c.

Fifth matching earns whatever (it shouldn't be more than $766, or about $900 if the bar tender get 15%, else positive for the player!)
EventProbabilityPaysContribution
3 not 4
.023148
$1
$0.02 315c
4 not 5
.003858
$100
$0.38 580c
5 jackpot
.000772
$901.18
$0.59 105c
$1.00 000c
unJon
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August 6th, 2022 at 1:24:38 PM permalink
Quote: charliepatrick

The maths sorts of works if you roll one die at a time and lose once you fail to get the recent roll to match.

The first roll is irrelevant. The second roll has to match the first roll to allow a third roll (P=1/6). The third roll has to match, else you lose. You earn a free roll (unless your fourth roll matches). (So the probability of this is 1/36 - 1/216 = 5/216, I have assumed you have the option of having your $1 returned for the break-even point.)

Fourth matching roll earns $100 (probability of this is 1 in 216, but you take off the probability of jackpot to give 5/1296) so this represents about 38.58c.

Fifth matching earns whatever (it shouldn't be more than $766, or about $900 if the bar tender get 15%, else positive for the player!)

EventProbabilityPaysContribution
3 not 4
.023148
$1
$0.02 315c
4 not 5
.003858
$100
$0.38 580c
5 jackpot
.000772
$901.18
$0.59 105c
$1.00 000c

link to original post



Excellent math sleuthing. Youíll get a more accurate result if instead of using $1 for 3OAK you just juice the probabilities of the 4OAK and 5OAK by the 102.3697%.

Basically the sum from n=1 to infinity of (5/216)^n.

ETA: oh I see, $1 for break even on 3OAK.
Last edited by: unJon on Aug 6, 2022
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
BillHasRetired
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August 6th, 2022 at 5:46:38 PM permalink
I don't think the original poster indicated that the dice were rolled one at a time, but all five were rolled at once. Not sure what effect it would have on your math, though.
charliepatrick
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August 7th, 2022 at 9:34:27 AM permalink
Quote: BillHasRetired

I don't think the original poster indicated that the dice were rolled one at a time, but all five were rolled at once...

As others have already stated it would be in the Player's advantage if you could roll all five dice rather than one at a time. This is why I was trying to work out a scenario where the game might made sense. Sadly the OP hasn't got back with a clarification of the exact rules and payouts.
SOOPOO
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August 7th, 2022 at 11:31:42 AM permalink
Quote: unJon

I take it back. The game doesnít make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldnít build, it should drain from the 4OAKs.

What am
I missing?
link to original post



You are missing the address of the pub! And yes, that is Axel at the end of the bar rolling the diceÖ.
Dieter
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August 7th, 2022 at 12:40:17 PM permalink
Quote: charliepatrick

Quote: BillHasRetired

I don't think the original poster indicated that the dice were rolled one at a time, but all five were rolled at once...

As others have already stated it would be in the Player's advantage if you could roll all five dice rather than one at a time. This is why I was trying to work out a scenario where the game might made sense. Sadly the OP hasn't got back with a clarification of the exact rules and payouts.
link to original post



1. I think you get to play once a day.
2. I think you have to buy a drink to be allowed to play.

The game may be positive, but I don't think it's profitable to the player.
That said, if you're down at the bar anyway...
May the cards fall in your favor.
Dieter
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August 7th, 2022 at 12:40:25 PM permalink
Quote: charliepatrick

Quote: BillHasRetired

I don't think the original poster indicated that the dice were rolled one at a time, but all five were rolled at once...

As others have already stated it would be in the Player's advantage if you could roll all five dice rather than one at a time. This is why I was trying to work out a scenario where the game might made sense. Sadly the OP hasn't got back with a clarification of the exact rules and payouts.
link to original post



1. I think you get to play once a day.
2. I think you have to buy a drink to be allowed to play.

The game may be positive, but I don't think it's profitable to the player.
That said, if you're down at the bar anyway...
May the cards fall in your favor.
avianrandy
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April 8th, 2023 at 6:36:29 AM permalink
Have you been back to the pub lately? What are the exact rules for this game?
darkoz
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April 8th, 2023 at 8:13:14 AM permalink
Being a bar pub game it may very well be +EV.

The OP said there is no rake other than the tip for the top payout. So basically a tip for a guest getting a jackpot of sorts

I think we are all too much into figuring out the negative EV.

The games positive EV for the house is simply that they drum up business for their pub, make an occasional jackpot winner happy (spreading the word) and they even get to share in that persons jackpot.

It also doesn't sound like an official game so maybe a negative expectation game would be illegal? Usually that's why a house doesn't take a rake

Also since it's players money going into the pot even though it's positive EV you would have to wait for it to get to a decent size. The object isn't to just win back your own money
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GenoDRPh
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April 8th, 2023 at 9:30:30 AM permalink
Quote: avianrandy

Have you been back to the pub lately? What are the exact rules for this game?
link to original post



Haven't been back since before COVID, A hospitalization, then COVID, then a move to another part of town. It was withing walking distance, and unless I know I'm going to just get one drink and nurse it all night I don't drink and get behind the wheel, so it's not worth the risk of a drive. If I even find myself back there, I'll be sure to inquire of the rules and update.
ThatDonGuy
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April 8th, 2023 at 12:29:09 PM permalink
Quote: darkoz

Being a bar pub game it may very well be +EV.
link to original post


Am I missing something obvious?
There are 7776 results from rolling 5 dice.
150 of them are four of a kind.
Even if any roll besides a four of a kind paid nothing, the EV is 150 x 100 / 7776 - 1 = 0.929.
NotSoFun21
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June 4th, 2024 at 9:23:48 PM permalink
sorry to revive this but something bothers me...

the triple DOES NOT pay $1 its WORTH $1. this is the same as a lotto giving a 'free ticket' instead of paying the $1. Since the $1 DOES NOT come out of the pot, the Triples chance is added back into the game AS POSTED. The Chance of ANY 5oK is still 6^5/6 = 6^4 = 1296. My 'corrected' pay is $796. After the15% tip, $676.6

I will offer another view...
4/5 = 100/216 (6^5/6)/6
the remaining fraction pays the 5/5 = $696... after the tip $591.6

There was a bar about 10mi. away (but up the street from where i worked) that had this exact game and pay. Its easy to think $1296 is B/E but the pays of 4oK lowers it. A rule of thumb is $700+ is AP.
Last edited by: NotSoFun21 on Jun 4, 2024
unJon
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June 5th, 2024 at 4:15:15 AM permalink
Quote: NotSoFun21

sorry to revive this but something bothers me...

the triple DOES NOT pay $1 its WORTH $1. this is the same as a lotto giving a 'free ticket' instead of paying the $1. Since the $1 DOES NOT come out of the pot, the Triples chance is added back into the game AS POSTED. The Chance of ANY 5oK is still 6^5/6 = 6^4 = 1296. My 'corrected' pay is $796. After the15% tip, $676.6

I will offer another view...
4/5 = 100/216 (6^5/6)/6
the remaining fraction pays the 5/5 = $696... after the tip $591.6

There was a bar about 10mi. away (but up the street from where i worked) that had this exact game and pay. Its easy to think $1296 is B/E but the pays of 4oK lowers it. A rule of thumb is $700+ is AP.
link to original post



Sorry Iím not following your middle paragraph. Whatís wrong with the logic that any amount above $100 is AP since $100 for 4OAK is +EV on its own?
Last edited by: unJon on Jun 5, 2024
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
NotSoFun21
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June 5th, 2024 at 2:50:02 PM permalink
the odds of 4/5 is 6*6*6*6*6 divided by the 6 ranks which is then divided by the 5 ways that the 4oK can occur = 7776/30
i made a mistake calculating this, and have clarified. the payment is 100/259.2 which is NOT AP, and further, it reduces the jackpot when hit.

The correct answer is based upon 1296 rolls of the dice.
The chance of 4 of 5 is 6*6*6*6*6/(6*5) = 1 in 259.2
There will be 125/648 fewer $'s in the pot because of the 'free rolls'.
So the JP at 100% payout is 1-(125/648+100/259.2) = 1 - 0.5787 = 0.4213 times 1296 = $546
You get 85% or $464
If you want to win 100% after the tip, the JP must be 546/0.85 = $642 or better.

sorry for the confusion and error
NSF21
Last edited by: NotSoFun21 on Jun 5, 2024
ThatDonGuy
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June 5th, 2024 at 4:11:29 PM permalink
Quote: NotSoFun21

the odds of 4/5 is 6*6*6*6*6 divided by the 6 ranks which is then divided by the 5 ways that the 4oK can occur = 7776/30

link to original post


Er, if you are counting every possible 4OAK, isn't it 6*6*6*6*6 divided by the 6 ranks and then divided by the 25 ways it can occur?
e.g. for four 6s:
1 6 6 6 6
2 6 6 6 6
3 6 6 6 6
4 6 6 6 6
5 6 6 6 6
6 1 6 6 6
6 2 6 6 6
6 3 6 6 6
6 4 6 6 6
6 5 6 6 6
6 6 1 6 6
6 6 2 6 6
6 6 3 6 6
6 6 4 6 6
6 6 5 6 6
6 6 6 1 6
6 6 6 2 6
6 6 6 3 6
6 6 6 4 6
6 6 6 5 6
6 6 6 6 1
6 6 6 6 2
6 6 6 6 3
6 6 6 6 4
6 6 6 6 5
NotSoFun21
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June 5th, 2024 at 4:44:24 PM permalink
thanks for that, i see the results you speak of. yes. So the odds are 6^5/150 not 30. Thus 1 in 51.84 (1/5 of my answer).
unJon
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June 5th, 2024 at 5:41:00 PM permalink
Quote: NotSoFun21

thanks for that, i see the results you speak of. yes. So the odds are 6^5/150 not 30. Thus 1 in 51.84 (1/5 of my answer).
link to original post



Right. Making it +EV from the get go as long as there is enough in the pot to pay out the 4OAK.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
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